Beginning on January 1, park rangers in Everglades National Park began recording the water level for one particularly dry area of the park. The water level was initially 2.5 ft and decreased by approximately 0.015 ft/day. a. Write a function representing the water level L x (in ft), x days after January 1. b. Write an equation for L − 1 x . c. What does the inverse handier, represent in the context of this problem? d. Evaluate L − 1 1.9 and interpret its meaning in context.
Beginning on January 1, park rangers in Everglades National Park began recording the water level for one particularly dry area of the park. The water level was initially 2.5 ft and decreased by approximately 0.015 ft/day. a. Write a function representing the water level L x (in ft), x days after January 1. b. Write an equation for L − 1 x . c. What does the inverse handier, represent in the context of this problem? d. Evaluate L − 1 1.9 and interpret its meaning in context.
Solution Summary: The author determines the function L(x) ( in ft ) which defines the water level x days after January 1.
Beginning on January 1, park rangers in Everglades National Park began recording the water level for one particularly dry area of the park. The water level was initially 2.5 ft and decreased by approximately 0.015 ft/day.
a. Write a function representing the water level
L
x
(in ft), x days after January 1.
b. Write an equation for
L
−
1
x
.
c. What does the inverse handier, represent in the context of this problem?
d. Evaluate
L
−
1
1.9
and interpret its meaning in context.
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3. We'd like to know the first time when the population reaches 7000 people. First, graph the
function from part (a) on your calculator or Desmos. In the same window, graph the line y =
7000. Notice that you will need to adjust your window so that you can see values as big as
7000! Investigate the intersection of the two graphs. (This video shows you how to find the
intersection on your calculator, or in Desmos just hover the cursor over the point.) At what
value t> 0 does the line intersect with your exponential function? Round your answer to two
decimal places. (You don't need to show work for this part.) (2 points)
College Algebra with Modeling & Visualization (5th Edition)
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